Question

Solve the following pair of equations:

$7x-8y=-12$

$-4x+2y=3$

• A. $x=0,y=0$
• B. $x=0,y=\frac{3}{2}$
• C. $x=\frac{5}{2},y=4$
• D. $x=6,y=\frac{1}{2}$

Answer 1

The correct option is B $x=0,y=\frac{3}{2}$

We have
$7x-8y=-12\dots \left(1\right)$
$-4x+2y=3\dots \left(2\right)$
Multiplying equation (1) by 4, we have

$28x-32y=-48...\left(3\right)$

Multiplying equation (2) by 7, we have

$-28x+14y=\mathrm{21...}\left(4\right)$

Adding equations (3) and (4), we get

$-18y=-27$

$\Rightarrow y=\frac{-27}{-18}=\frac{3}{2}$

Putting $y=\frac{3}{2}$ in equation 2, we get

$-4x+2\times \frac{3}{2}=3$

$\Rightarrow -4x=0$

$\Rightarrow x=0$